Curriculum  /  Math  /  7th Grade  /  Unit 2: Operations with Rational Numbers  /  Lesson 14

Operations with Rational Numbers

Lesson 14

Math

Unit 2

7th Grade

Lesson 14 of 18

Objective

Determine the rules for dividing signed numbers.

Common Core Standards

Core Standards

  • 7.NS.A.2.B — Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.
  • 7.NS.A.2.C — Apply properties of operations as strategies to multiply and divide rational numbers.

Foundational Standards

  • 5.NF.B.3
  • 3.OA.B.6

Criteria for Success

  1. Use the relationship between multiplication and division to determine the rules for dividing signed numbers (MP.8).
  2. Write division problems of signed numbers as multiplication problems, and vice versa.
  3. Understand that the division problem $${p \div q}$$, where $$p$$ and $$q$$ are integers and $$q \neq 0$$, can be represented as $$p\over q$$, and vice versa. 
  4. Understand that for integers $$p$$ and $$q$$, where $$q \neq 0$$, the following are equivalent: $$-{p\over q} = {-p\over q} = {p\over-q}$$.

Tips for Teachers

  • Lessons 14 and 15 address dividing signed numbers. Lesson 14 introduces the concept and Lesson 15 involves real-world applications.
  • The equivalence between $$-\frac{p}{q}$$, $$\frac{-p}{q}$$, and $$\frac{p}{-q}$$ is an important concept for students to understand when they study slope, the change in $$y$$ values over the change in $$x$$ values for a linear relationship, in 8th grade.
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Anchor Problems

25-30 minutes

Problem 1

Four multiplication problems are shown in the table. Write each one as a division problem and then find the solution. What can you conclude about the rules for dividing signed numbers?

Multiplication Problem Division Problem Solution
$$2\times\square=6$$ $$6\div2=\square$$

$$\square=$$
$$2\times\square=-6$$  

$$\square=$$
$$-2\times\square=-6$$  

$$\square=$$
$$-2\times\square=6$$  

$$\square=$$

Guiding Questions

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Student Response

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Problem 2

Write each division problem as a fraction, and then find each quotient. What do you notice about the three problems? Why do you think this happened?

a.   $$-24 \div 6$$

b.   $$24 \div (-6)$$

c.   $$-(24\div6)$$

Guiding Questions

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Student Response

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Problem 3

Which expressions are equivalent to $${5\div (-12)}$$? Select all that apply.

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Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.

a.   $$-0.25$$ and $$\frac{1}{-4}$$

b.   $$-\left ( \frac{1}{4} \right )$$ and $$\frac{-1}{-4}$$

c.   $$\frac{-1}{4}$$ and $$-\frac{1}{4}$$

Student Response

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems where students determine if the quotient will be positive or negative, without computing.
  • Include problems where students write or identify equivalent expressions, similar to Anchor Problem #3.
  • Include problems where students find the quotient, involving either integer or fraction answers (decimal representation is coming up in Lesson 16).

Next

Divide signed rational numbers and interpret quotients in real-world contexts.

Lesson 15
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Adding and Subtracting Rational Numbers

Topic B: Multiplying and Dividing Rational Numbers

Topic C: Using all Four Operations with Rational Numbers

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